Abstract
In polycrystalline materials, dislocations can interact with grain boundaries (GBS) through a number of mechanisms including dislocation absorption, pile-up formation, dissociation reactions within the GB plane and (possibly) dislocation nucleation from the interface itself. The effects of dislocation pile-ups contribute significantly to the mechanical behavior of polycrystalline materials by creating back-stresses that inactivate the primary slip systems in the vicinity of the interface, corresponding with the celebrated Hall–Petch relationship between size and strength. However, dislocation pile-ups cannot be contained within the small grain sizes that can be accommodated by molecular dynamics simulations, which to-date remain the primary computational method used to study the discrete structure of GBs.
Dislocation dynamics (DD) simulations are a promising framework for computational modeling that are used to provide insights about phenomena that can only be explained from the intermediate scale between atomistic and macro scales. However, a robust framework for modeling dislocation interactions with internal microstructure such as grain boundaries (GBs) has yet to be achieved for 3D models of DD. Furthermore, this is the first implementation which explicitly includes the dislocation content of the interface. The framework described in this paper is effective for studying GB-dislocation interactions (including inter-granular effects) and the approach for partitioning the DD simulation domain. To achieve a robust method to differentiate between crystal regions, the present framework utilizes a mesh-based partitioning system. Within each grain, slip systems are determined by the grain orientation. The versatile construction described, allows modeling of an arbitrary crystallography, size and grain geometry. Extrinsic dislocations that intersect the interface are constrained to glide on the line of intersection between the glide plane and GB plane. Atomistically informed criteria for slip transmission are implemented, based on the geometrically optimal outgoing glide plane which shares a common line of intersection on the GB plane. Slip transmission is only initiated when the resolved shear stress in one of the compatible outgoing slip directions exceeds an approximate threshold resolved shear stress, which is based on observations made with molecular dynamics studies.
The primary aim of the present study was to establish a sufficiently ‘generic’ framework to enable the modelling of various GB structures, polycrystal geometries and crystallographic orientations. The framework described in the present work provides a means to study multi-grain deformation processes governed by dislocations pile-ups at GBs, in detail beyond feasible limits of experiments or atomistic simulation approaches.